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Hidden Markov models for zero-inflated Poisson counts with an application to substance use

Authors

  • Stacia M. DeSantis,

    Corresponding author
    1. Division of Biostatistics and Epidemiology, Medical University of South Carolina, U.S.A.
    • Division of Biostatistics and Epidemiology, Department of Medicine, Medical University of South Carolina, 135 Cannon Street, Charleston, SC 29425, U.S.A.
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  • Dipankar Bandyopadhyay

    1. Division of Biostatistics and Epidemiology, Medical University of South Carolina, U.S.A.
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Abstract

Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to ‘high’ or ‘low’ use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data. Copyright © 2011 John Wiley & Sons, Ltd.

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